The Structure of Commutative Semigroups With the Ideal Retraction Property

Abstract

This paper presents a complete characterization of commutative semigroups with the ideal retraction property. These semigroups are those with the property that each ideal is a homomorphic retraction of the semigroup. The fundamental building blocks of these semigroups are the 2-cores and the semilattice of idempotents. Structure for semilattices with the ideal retraction property was discussed in an earlier paper and the structure of the 2-core is described in detail within this paper